Density of positive Lyapunov exponents for symplectic cocycles (Q2327710)

Summary: We prove that \(\mathrm{Sp}(2d,\mathbb R)\)-cocycles, \(\mathrm{HSp}(2d)\)-cocycles and pseudo-unitary cocycles with at least one non-zero Lyapunov exponent are dense in all usual regularity classes for non periodic dynamical systems. For Schrödinger operator on the strip, we prove a similar result for density of positive Lyapunov exponents. This generalizes a result of \textit{A. Avila} [J. Am. Math. Soc. 24, No. 4, 999--1014 (2011; Zbl 1236.37031)] to higher dimensions.